The British public will not accept a Brexit deal that leaves them worse off financially, a new poll suggests. In a sign that a majority of the public would be unwilling to accept an economically damaging hard Brexit, half of those who voted to leave the EU in June, including 62% of Labour voters and 59% of those in the north, would not be willing to lose any money at all as a consequence of Britain’s withdrawal.

Just one in 10 would be willing to lose more than £100 a month. Pollster Peter Kellner, the former president of YouGov, said the results suggested that Theresa May “could have real difficulty in delivering a Brexit that satisfies those who voted for it”.

He added: “This is the first poll to look specifically at whether leave voters are willing to accept any financial loss as a result of Brexit. The answer is that few are prepared to.”

The £350m battle bus – one of the defining images of the EU referendum. Photograph: Stefan Rousseau/PA

Another poll, by consumer magazine Which?, also indicates that the economic effects of Brexit are a major worry for much of the public. It shows that almost half the population (47%) are worried about Brexit, up eight points since September, with nearly two-thirds concerned about its potential impact on food prices.

Brexit voters in areas where a majority of people backed EU withdrawal are among those most unhappy to be left worse off, according to the study – including 59% in the north and 54% in Wales and the Midlands.

Even among Ukip supporters – whose party has demanded May reject the article 50 process and instead leave the EU immediately by repealing the 1972 European Communities act – a substantial number, 39%, do not want to incur a financial loss because of Brexit.

Campaigners in favour of a soft Brexit believe the findings could convince the government to think again on potential plans to pull out of the single market – and could reignite a contentious debate over whether Brexit voters were aware that their ballots meant leaving the single market.

Lib Dem leader Tim Farron has warned that the British public do not want a hard Brexit ‘at any cost’. Photograph: Gareth Fuller/PA

The Liberal Democrat leader, Tim Farron, said: “It’s clear the British public don’t want a hard Brexit at any cost, despite what the Tories might think. They no longer support membership of the single market and have given up on people who don’t wish to sign away a blank cheque Brexit.”

A leaked memo from a meeting between Brexit secretary David Davis and the City of London Corporation last month implied that the EU’s “inflexible” approach to the free movement of people meant it was “unlikely the UK would achieve access”.

Open Britain’s poll also suggests that the prolonged period of uncertainty since the 23 June referendum has chipped away at the pro-Brexit majority. If a rerun of the vote were held tomorrow, remain and leave would be tied at 44% each, with 5% not voting at all and 7% undecided.